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Existence of Solutions for Vector Optimization on Hadamard Manifolds

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Abstract

In this paper, a relationship between a vector variational inequality and a vector optimization problem is given on a Hadamard manifold. An existence of a weak minimum for a constrained vector optimization problem is established by an analogous to KKM lemma on a Hadamard manifold.

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Acknowledgements

The authors are grateful to the editor and the referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (11171237) and the Key Program of NSFC (Grant No. 70831005).

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, P.R. China

    Li-Wen Zhou & Nan-Jing Huang

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  1. Li-Wen Zhou
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  2. Nan-Jing Huang
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Correspondence to Nan-Jing Huang.

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Communicated by Byung-Soo Lee.

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Zhou, LW., Huang, NJ. Existence of Solutions for Vector Optimization on Hadamard Manifolds. J Optim Theory Appl 157, 44–53 (2013). https://doi.org/10.1007/s10957-012-0186-3

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  • DOI: https://doi.org/10.1007/s10957-012-0186-3

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